Deformation of Earth Materials Much of the recent progress in the solid Earth sciences is based on the interpretation of a range of geophysical and geological observations in terms of the properties and deformation of Earth materials One of the greatest challenges facing geoscientists in achieving this lies in finding a link between physical processes operating in minerals at the smallest length scales to geodynamic phenomena and geophysical observations across thousands of kilometers This graduate textbook presents a comprehensive and unified treatment of the materials science of deformation as applied to solid Earth geophysics and geology Materials science and geophysics are integrated to help explain important recent developments, including the discovery of detailed structure in the Earth’s interior by high-resolution seismic imaging, and the discovery of the unexpectedly large effects of high pressure on material properties, such as the high solubility of water in some minerals Starting from fundamentals such as continuum mechanics and thermodynamics, the materials science of deformation of Earth materials is presented in a systematic way that covers elastic, anelastic, and viscous deformation Although emphasis is placed on the fundamental underlying theory, advanced discussions on current debates are also included to bring readers to the cutting edge of science in this interdisciplinary area Deformation of Earth Materials is a textbook for graduate courses on the rheology and dynamics of the solid Earth, and will also provide a much-needed reference for geoscientists in many fields, including geology, geophysics, geochemistry, materials science, mineralogy, and ceramics It includes review questions with solutions, which allow readers to monitor their understanding of the material presented S H U N - I C H I R O K A R A T O is a Professor in the Department of Geology and Geophysics at Yale University His research interests include experimental and theoretical studies of the physics and chemistry of minerals, and their applications to geophysical and geological problems Professor Karato is a Fellow of the American Geophysical Union and a recipient of the Alexander von Humboldt Prize (1995), the Japan Academy Award (1999), and the Vening Meinesz medal from the Vening Meinesz School of Geodynamics in The Netherlands (2006) He is the author of more than 160 journal articles and has written/edited seven other books Deformation of Earth Materials An Introduction to the Rheology of Solid Earth Shun-ichiro Karato Yale University, Department of Geology & Geophysics, New Haven, CT, USA CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521844048 © S Karato 2008 This publication is in copyright Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published in print format 2008 ISBN-13 978-0-511-39478-2 eBook (NetLibrary) ISBN-13 hardback 978-0-521-84404-8 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Contents Preface page ix Part I General background 1 Stress and strain 3 1.1 Stress 1.2 Deformation, strain Thermodynamics 2.1 2.2 2.3 2.4 Thermodynamics of reversible processes Some comments on the thermodynamics of a stressed system Thermodynamics of irreversible processes Thermally activated processes Phenomenological theory of deformation 3.1 3.2 3.3 3.4 3.5 Part II Classification of deformation Some general features of plastic deformation Constitutive relationships for non-linear rheology Constitutive relation for transient creep Linear time-dependent deformation 34 34 35 36 38 39 Materials science of deformation 49 Elasticity 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Introduction Elastic constants Isothermal versus adiabatic elastic constants Experimental techniques Some general trends in elasticity: Birch’s law Effects of chemical composition Elastic constants in several crystal structures Effects of phase transformations Crystalline defects 5.1 5.2 5.3 5.4 13 13 28 29 32 Defects and plastic deformation: general introduction Point defects Dislocations Grain boundaries Experimental techniques for study of plastic deformation 6.1 Introduction 6.2 Sample preparation and characterization 51 51 52 55 57 59 67 70 72 75 75 76 82 94 99 99 99 v vi Contents Control of thermochemical environment and its characterization Generation and measurements of stress and strain Methods of mechanical tests Various deformation geometries 102 104 108 112 Brittle deformation, brittle–plastic and brittle–ductile transition 114 114 115 118 6.3 6.4 6.5 6.6 7.1 Brittle fracture and plastic flow: a general introduction 7.2 Brittle fracture 7.3 Transitions between different regimes of deformation Diffusion and diffusional creep 8.1 8.2 8.3 8.4 8.5 Fick’s law Diffusion and point defects High-diffusivity paths Self-diffusion, chemical diffusion Grain-size sensitive creep (diffusional creep, superplasticity) Dislocation creep 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 General experimental observations on dislocation creep The Orowan equation Dynamics of dislocation motion Dislocation multiplication, annihilation Models for steady-state dislocation creep Low-temperature plasticity (power-law breakdown) Deformation of a polycrystalline aggregate by dislocation creep How to identify the microscopic mechanisms of creep Summary of dislocation creep models and a deformation mechanism map 10 Effects of pressure and water 10.1 Introduction 10.2 Intrinsic effects of pressure 10.3 Effects of water 11 Physical mechanisms of seismic wave attenuation 11.1 11.2 11.3 11.4 Introduction Experimental techniques of anelasticity measurements Solid-state mechanisms of anelasticity Anelasticity in a partially molten material 12 Deformation of multi-phase materials 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 Introduction Some simple examples More general considerations Percolation Chemical effects Deformation of a single-phase polycrystalline material Experimental observations Structure and plastic deformation of a partially molten material 13 Grain size 13.1 13.2 13.3 13.4 Introduction Grain-boundary migration Grain growth Dynamic recrystallization 123 123 125 126 127 129 143 143 145 145 154 157 161 162 164 164 168 168 169 181 199 199 199 202 210 214 214 215 216 222 225 225 225 227 232 232 233 236 243 Contents vii 13.5 Effects of phase transformations 13.6 Grain size in Earth’s interior 14 Lattice-preferred orientation 14.1 14.2 14.3 14.4 14.5 Introduction Lattice-preferred orientation: definition, measurement and representation Mechanisms of lattice-preferred orientation A fabric diagram Summary 15 Effects of phase transformations 15.1 15.2 15.3 15.4 15.5 15.6 Introduction Effects of crystal structure and chemical bonding: isomechanical groups Effects of transformation-induced stress–strain: transformation plasticity Effects of grain-size reduction Anomalous rheology associated with a second-order phase transformation Other effects 16 Stability and localization of deformation 16.1 16.2 16.3 16.4 16.5 Introduction General principles of instability and localization Mechanisms of shear instability and localization Long-term behavior of a shear zone Localization of deformation in Earth Part III Geological and geophysical applications 17 Composition and structure of Earth’s interior 17.1 17.2 17.3 17.4 Gross structure of Earth and other terrestrial planets Physical conditions of Earth’s interior Composition of Earth and other terrestrial planets Summary: Earth structure related to rheological properties 18 Inference of rheological structure of Earth from time-dependent deformation 18.1 Time-dependent deformation and rheology of Earth’s interior 18.2 Seismic wave attenuation 18.3 Time-dependent deformation caused by a surface load: post-glacial isostatic crustal rebound 18.4 Time-dependent deformation caused by an internal load and its gravitational signature 18.5 Summary 19 Inference of rheological structure of Earth from mineral physics 19.1 Introduction 19.2 General notes on inferring the rheological properties in Earth’s interior from mineral physics 19.3 Strength profile of the crust and the upper mantle 19.4 Rheological properties of the deep mantle 19.5 Rheological properties of the core 20 Heterogeneity of Earth structure and its geodynamic implications 20.1 Introduction 20.2 High-resolution seismology 20.3 Geodynamical interpretation of velocity (and attenuation) tomography 249 253 255 255 256 262 268 269 271 271 271 280 286 286 287 288 288 289 293 300 300 303 305 305 306 314 322 323 323 324 326 331 337 338 338 339 342 358 361 363 363 364 370 viii Contents 21 Seismic anisotropy and its geodynamic implications 21.1 21.2 21.3 21.4 21.5 21.6 Introduction Some fundamentals of elastic wave propagation in anisotropic media Seismological methods for detecting anisotropic structures Major seismological observations Mineral physics bases of geodynamic interpretation of seismic anisotropy Geodynamic interpretation of seismic anisotropy References Materials index Subject index The colour plates are between pages 118 and 119 391 391 392 398 401 402 407 412 452 454 Preface Understanding the microscopic physics of deformation is critical in many branches of solid Earth science Long-term geological processes such as plate tectonics and mantle convection involve plastic deformation of Earth materials, and hence understanding the plastic properties of Earth materials is key to the study of these geological processes Interpretation of seismological observations such as tomographic images or seismic anisotropy requires knowledge of elastic, anelastic properties of Earth materials and the processes of plastic deformation that cause anisotropic structures Therefore there is an obvious need for understanding a range of deformation-related properties of Earth materials in solid Earth science However, learning about deformation-related properties is challenging because deformation in various geological processes involves a variety of microscopic processes Owing to the presence of multiple deformation mechanisms, the results obtained under some conditions may not necessarily be applicable to a geological problem that involves deformation under different conditions Therefore in order to conduct experimental or theoretical research on deformation, one needs to have a broad knowledge of various mechanisms to define conditions under which a study is to be conducted Similarly, when one attempts to use results of experimental or theoretical studies to understand a geological problem, one needs to evaluate the validity of applying particular results to a given geological problem However, there was no single book available in which a broad range of the physics of deformation of materials was treated in a systematic manner that would be useful for a student (or a scientist) in solid Earth science The motivation of writing this book was to fulfill this need In this book, I have attempted to provide a unified, interdisciplinary treatment of the science of deformation of Earth with an emphasis on the materials science (microscopic) approach Fundamentals of the materials science of deformation of minerals and rocks over various time-scales are described in addition to the applications of these results to important geological and geophysical problems Properties of materials discussed include elastic, anelastic (viscoelastic), and plastic properties The emphasis is on an interdisciplinary approach, and, consequently, I have included discussions on some advanced, controversial issues where they are highly relevant to Earth science problems They include the role of hydrogen, effects of pressure, deformation of two-phase materials, localization of deformation and the link between viscoelastic deformation and plastic flow This book is intended to serve as a textbook for a course at a graduate level in an Earth science program, but it may also be useful for students in materials science as well as researchers in both areas No previous knowledge of geology/ geophysics or of materials science is assumed The basics of continuum mechanics and thermodynamics are presented as far as they are relevant to the main topics of this book Significant progress has occurred in the study of deformation of Earth materials during the last $30 years, mainly through experimental studies Experimental studies on synthetic samples under well-defined chemical conditions and the theoretical interpretation of these results have played an important role in understanding the microscopic mechanisms of deformation Important progress has also been made to expand the pressure range over which plastic deformation can be investigated, and the first low-strain anelasticity measurements have been conducted In addition, some large-strain deformation experiments have been performed that have provided important new insights into the microstructural evolution during deformation However, experimental data are always obtained under limited conditions and their applications to the Earth involve large extrapolation It is critical to understand ix ... states that the change in the internal energy, dE, is the sum of the mechanical work done to the system, the change in the energy due to the addition of materials and the heat added to the system,... Deformation of Earth Materials An Introduction to the Rheology of Solid Earth Shun-ichiro Karato Yale University, Department of Geology & Geophysics, New Haven, CT, USA CAMBRIDGE UNIVERSITY PRESS. .. ‘‘heat’’ is the change in energy other than the mechanical work and energy caused by the exchange of material These two quantities (mechanical work and the energy associated with the transport of matter)